There are several factors worth addressing here, and I don't necessarily want to start a calibre discussion here because, basically, my view is that if you are bias towards one calibre over another for whatever reason you will never be satisfied unless you are shooting that calibre, or unless you experience both and make an informed choice based on that experience.
I use springers and PCPs in both calibres and .177 is my mainstream in almost all cases, the main exception being shooting in and around farm buildings at closer ranges, where a hollow or flat .22 is great on rats and feral pigeons without the same potential for property damage as the .177, which can often shoot straight through and keep going at shorter ranges.
The primary issues you should really address is whether you prefer a heavier or a lighter gun. This is entirely personal and has little to do with your physical build.
Women make ideal candidates when kitting up with guns or bows, because if something is too heavy they will tell you straight away. Men do the reverse and often introduce problems as a result. The number of guys I have made longbows for who struggle to draw them is a nonsense, when they went and told you they could confortably shoot waayyyyyyyyyyyyyy more weight than they can actually handle. Guns tend to be similar in that a lot of people argue the case for a heavier gun. I don't really buy into a heavy air rifle damping recoil, on the basis that most airguns have so little recoil that the physical weight of the gun is far less important than a firm and controlled hold with good shot follow through.
I have tried heavier guns and over the years found that I shoot better over longer, more sustained sessions with a lighter rifle - I am 6' 4" and about 230 pounds, but you can keep your HW80, 97, 90 and so on. I also don't enjoy carting a heavier gun around if I am out on a long lamping session, while the lighter gun is a pleasure rather than an inconvenient chore.
If you want to buy new you could do far worse than the lighter Weihrauch guns. The HW95K and the HW99S are both very light spring powered break barrels and they fall well within your budget. They have the best (arguably) off-the-shelf trigger unit there is and if you can't shoot well with one you shouldn't be shooting at all. They can outperform the majority of shooters who will ever own one.
I have a Venom tuned .177 HW95K and it is by far the single best springer for game-getting that I have ever owned by a very long margin. Even with a scope and scope mounted lamp it is an easy weapon to carry and use over extended periods.
You also need to extend your considerations into optics: I would suggest a fixed magnification 6x40 or 8x40 scope with low mounts. Low mounts put the line of barrel and line of scope closer together and a fixed mag scope takes away the faff factor and the temptation to monkey with your kit instead of shoot with it. If you buy a 3-9x40 then crank it up to 6x and leave it there. Larger objective lenses require higher mounts making zero a little more difficult (this is marginal, to be fair) but the larger objective lens scopes can introduce the potential for greater parallax. Basically there isn't much you can't do in the field with a good 6x40, 8x40 or a 3-9x40 (if left cranked up to 6x). A fixed 4x40 is OK but a 6x or 8x40 is much, much better in most conditions apart from extremely low light.
Steer clear of parallax adjusting scopes until you are putting supper on the table and consistently putting in 10 shots within a 10 penny piece out to 30 - 35 yards. There's no sense in paying more for a scope that you have to monkey with instead of just shooting with the darn thing, and my view is that you shouldn't rely on a scope for judging distance - this is such a vital part of airgun shooting and if you can't learn to judge your distances out to 30 - 35 yards or so then, again, you shouldn't be shooting.
No matter what kit you buy, practice, practice, and practice some more.
Accuracy is obviously key to successful airgun shooting and I always try and practice more where I am weakest (standing shots) and less where I am strongest (kneeling).
You don't need to break the bank but you do have to ask some very telling questions of yourself to give yourself the very best chance right out of the blocks.
Some time ago I went to a local gunshop on a mission to buy a new (and very expensive) PCP air rifle. After shouldering said gun I knew on the first attempt it wasn't going to work out and I ended up buying a much lighter, far less expensive model that felt very comfortable in the shoulder from the outset - it was a little Air Arms S200. Aside from the financial difference (in my favour) I can knock nails in with that little gun - some folks have raised an eyebrow when they see someone of my size and shape using it, but I couldn't give a fig about that - the results I enjoy are a great indicator that I made the right choice...
I'd spend some time at your local gunshop and shoulder a few rifles within your price bracket and go from there. I've spent fortunes over the years buying on recommendation or reputation (or both) but I enjoy my shooting far more and have better results by going my own way.
Have a think, then think a bit more, before making your move.
Good luck with it - I hope you get as much out of your airgun shooting as I have had
I'll get my coat...
